Solar installation trend in Seattle

Why is there a drop in residential solar installation in Seattle from 2016? The study area is Seattle and the unit of analysis is census track.

Solar installation trend by contractors

Residential households in Seattle

Residential solar potential (MWh/ household) in Seattle

Residential solar potential (MWh) in Seattle

There are two noticeable groups in social characteristics with solar potential (MWh): A group of high income, single family housing owners and a group of low income, multifamily housing renters. These two groups have comparatively higher potential for solar electricity generation.

Boxplot for overall potential solar

Histograms of multiple variables

Variables are collected through several datasets including National Renewable Energy Laboratory (NREL) REPLICA 2018, American Community Survey (ACS) 2011 - 2015, the Department of Housing and Urban Development (HUD) 2017 and City of Seattle open data portal.

Cor plot

The proportion of solar installation per housing unit is the dependent variable (sol_instl) per census track. Rest of variables are as follows.

  • hu_own: a proportion of owner-occupied housing units
  • hu_blt1970: a proportion of housing units built before 1970
  • hu_no_mor: a proportion of housing units without a mortgage
  • hu_med_val: median value of owner-occupied housing units
  • hu_ex_1000: a proportion of owner-occupied units with housing costs greater than $1000/month
  • edu: a proportion of over 25 year old population with college degree and above
  • wh_race: a proportion of Caucasian population
  • hh_med_income: household median income
  • hh_gini_index: household GINI Index of income inequality
  • lihtc: low income tax credit qualification (T/F)
  • hh_high_sf_own: a proportion of households of high income, single family housing owners
  • hu_mwh: solar energy potential (MWh) per housing unit in a census track

The dependent variable (sol_instl) is correlated to all the variables except for the household GINI index and LITHC qualification.

Regression

By exploratory regression analyses, the best model with the highest R-squared (0.61) and lowest AIC (653.69) was chosen with the two variables, hu_med_val and hu_ex_1000 through OLS.

  sol instl
Predictors Estimates CI p
(Intercept) -1.98 -3.58 – -0.39 0.016
hu med val 0.00 0.00 – 0.00 0.048
hu ex 1000 17.68 14.56 – 20.80 <0.001
Observations 131
R2 / adjusted R2 0.614 / 0.608

Residual from the OLS

The residual plot shows it is biased and clustered indicating the model is not catching well the variability of the dependent variable.

OLS residual mapping

OLS residual mapping

Geographically weighted regression (GWR)

Another method named Geographically Weighted Regression (GWR) was performed with the outcomes of R-squared (0.76) and AIC (625.54), which are better than the previous OLS model. Residual map shows random pattern as confirmed by auto correlation analysis with Moran’s index of 0.028 and z-score of 0.75.

Residual mapping for GWR

Residual mapping for GWR

Geographically weighted impact

This model tells that the median value of owner-occupied housing units predicts residential solar installation more in the area of darker red as below. These areas are more sensitive to the median value of owner-occupied housing units with respect to the residential solar installation.

Impact of housing median value

Impact of housing median value

For the variable, total number of owner-occupied units with housing costs greater than $1000/month, the more sensitive areas are presented as darker red in the map below.

impact of housing cost over $1k/ month

impact of housing cost over $1k/ month

Hotspot analysis of residential solar installation

Each point represents the house unit with residential solar system installed on its building since 2003. By aggregating these points to the census track they are located in, hotspot areas and outliers were identified as below.

Solar installation hotspot

Solar installation hotspot

Solar installation outlier

Solar installation outlier

Factor analysis (Parallel screen)

It would be useful to include all the variables for a model rather than selecting only two variables. With a factor analysis, all the variables would be used for the model identification. The parallel screen confirms 2 or 3 factors would be appropriate.

## Parallel analysis suggests that the number of factors =  2  and the number of components =  NA

Factor analysis (Plot)

The 3 factors partially explain each variable depending on the latent characteristics.

Factor analysis (Diagram)

The first factor (ML1) is more related to the higher housing stability (homeownership), the 2nd factor (ML2) to the higher economic status, and the 3rd factor (ML3) is more related to the higher income inequality.

Factor correlation for solar installation

The most loaded, ML1 is positively correlated with the solar installation variable.

## [1] 131   3

Factor regression

The value of R-squared of the factor regression is the same as the previous OLS (0.61).

  regrs[[14]]
Predictors Estimates CI p
(Intercept) 5.09 4.59 – 5.59 <0.001
dat[,1] 3.34 2.67 – 4.02 <0.001
dat[,2] 0.64 0.02 – 1.25 0.044
dat[,3] 0.39 -0.23 – 1.01 0.217
Observations 131
R2 / adjusted R2 0.611 / 0.601

Cluster within cluster sum of squares (WCSS)

A cluster analysis was done to further study the featured census tracks. It shows clustering three would be appropriate.

Cluster analysis

## 
##  1  2  3 
## 55 32 44

## [1] 177.3648

Cluster plot

Based on the 3 factors, 3 clusters are presented in colors.

3D plot

3 clusters in Seattle

Each census track in Seattle was identified with the 3 clusters.

Clustered census track

Clustered census track

Cluster with boxplot

Each cluster shows unique features. Green groups comparatively have less housing stability and economic status while higher income inequality. Light blue groups are relatively opposite to the green groups. Light red groups keep their position in the middle of these 2 groups.

Cluster plot with smooth

Residential solar installation pattern in terms of clustering groups

Residential solar installation is exactly showing the same pattern of the 1st factor (ML1), the housing stability in clustering, which confirms the factor, ML1 has a predictive power for the residential solar installation.

Residential solar installation in Low Income Tax Credit

It indicates that lower solar installation proprotion and lower proportion of owner-occupied units with housing costs greater than $1000/month match the pattern of the certified LIHTC census tracks (TRUE).

Residential solar installation in housing unit median value

Higher solar installation is correlated with higher housing unit median value. Cluster #3, #1 and #2 in order are more likely to have higher solar installation.

Cumulative solar installation per census track

Time series analysis will help to understand the spatial-temporal pattern of residential solar installation in Seattle. Interestingly, one census track is noticeably high in installation over the period.

Residential solar installation trend in Seattle

Two different patterns of cumulative installation and annual new installation, are mapped in each census track in Seattle. It shows the pattern of cumulative number of installation is different from the annual new installation in that every year has a different installation trend depending on census tracks. In addition, hotspot outlier analysis was performed for the annual new installation map.

Spatial-temporal installation in Seattle

Spatial-temporal installation in Seattle

Spatial-temporal hotspot analysis

The difference between cumulative number of installation hotspot and annual new installation hotspot shows the emerging area of increasing installation pattern in residential solar. It is noticeable that West Seattle recently increases the installation while Ballad used to the one, then went slow, currently increases also. Columbia city presents that it has been and currently goes slow while the toal amount installation is still the highest in Seattle. It’s found that these areas are all clustered as light red (#1) and light blue (#3).

Hotspot for spatial-temporal cumulative installation in Seattle

Hotspot for spatial-temporal cumulative installation in Seattle

Hotspot for spatial-temporal annual installation in Seattle

Hotspot for spatial-temporal annual installation in Seattle

Takeaways

Residential solar installation follows patterns of

  • Housing median value
  • The number of owner-occupied house with higher housing cost

Cluster and factor analysis captures solar installation pattern (Cluster #1 and #3) in terms of

  • Higher housing stability
  • Higher economic status
  • Lower income inequality

Temporal pattern was also captured such that three noticeable areas were identified

  • Ballad – used to be a hotspot area, then went slow, currently seems increasing in solar installation
  • West Seattle – a new emerging area in solar installation
  • Columbia city – has been and currently goes slow. The toal amount installation is still the highest in Seattle.